I think there is a mistake in your question! Why? Because:
[A * B]/2 CANNOT EQUAL (A + B), and A and B be legs of a right triangle. You can have: A=3 and B=6 and
[6 x 3]/2 ==6 + 3. But 6, and 3 CANNOT be legs of a right triangle, because their sum SQUARED, 6^2 + 3^2 ==PERFECT square. In this case, they wqual (45), which not a pefect square.
Your question should read: "A right triangle with integer leg lengths is called cool if the number of square units in its area is equal to [TWICE (OR 3 TIMES)] the number of units in the sum of the lengths of its legs.